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http://functions.wolfram.com/06.10.03.0017.01
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Pochhammer[1/2, n] == (2 n - 1)!/(2^(2 n - 1) (n - 1)!)
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Cell[BoxData[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "n"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "n"]], "-", "1"]], ")"]], "!"]], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["2", "n"]], "-", "1"]]], RowBox[List[RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]], "!"]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "n"], Pochhammer] </annotation> </semantics> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Pochhammer </ci> <cn type='rational'> 1 <sep /> 2 </cn> <ci> n </ci> </apply> <apply> <times /> <apply> <factorial /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <factorial /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]], ")"]], "!"]], RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["2", " ", "n"]], "-", "1"]]], " ", RowBox[List[RowBox[List["(", RowBox[List["n", "-", "1"]], ")"]], "!"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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